Two convex lenses of focal length $$20$$ cm each are placed coaxially with a separation of $$60$$ cm between them. The image of the distant object formed by the combination is at _____ cm from the first lens.

$$\text{For the first lens: } u_1 = -\infty, \ f_1 = 20\text{ cm} \implies \frac{1}{v_1} - \frac{1}{-\infty} = \frac{1}{20} \implies v_1 = 20\text{ cm}$$

$$\text{The first image forms } 20\text{ cm to the right of the first lens, acting as the object for the second lens.}$$

$$\text{For the second lens: } u_2 = v_1 - d = 20 - 60 = -40\text{ cm}, \ f_2 = 20\text{ cm}$$

$$\frac{1}{v_2} - \frac{1}{u_2} = \frac{1}{f_2} \implies \frac{1}{v_2} - \frac{1}{-40} = \frac{1}{20} \implies \frac{1}{v_2} = \frac{1}{20} - \frac{1}{40} = \frac{1}{40} \implies v_2 = 40\text{ cm}$$

$$\text{Distance of the final image from the first lens: } D = d + v_2 = 60 + 40 = 100\text{ cm}$$